Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis . A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $s^ {-2}$ is

• A. 25 N
• B. 50 N
• C. 78.5 N
• D. 157 N

Answer 1

Answer: (D)

157 N

Answer 2

Here, mass of the cylinder, M = 50 kg
Radius of the cylinder, R = 0.5 m
Angular acceleration, $\alpha = 2\, rev\, s^{-2}$
$2 \times 2 \pi \,rad\, s^{-2} = 4 \pi\, rad\,s^{-2}$
Torque, $\tau = TR$
Moment of inertia of the solid cylinder about its axis, $I = \frac{1}{2} MR^2$
$\therefore$ Angular acceleration of the cylinder
$\alpha = \frac{\tau}{1} = \frac{TR}{\frac{1}{2}MR^2}$
$T = \frac{MR\alpha}{2} = \frac{50 \times 0.5 \times 4 \pi}{2} = 157 N$